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There have been many articles written on the psychological aspects of dealing with the inevitable losing runs that you will encounter if you gamble.

But one of the most important aspects of getting your head around a losing run psychologically is to know the worst losing sequence you can expect. This is generally termed the ELS (expected losing sequence) and the formula for calculating it is shown below, but firstly consider the following two systems:

1.       System 1 – it has a winning strike rate of 20% and long term has made 50% POT and is expected to continue to make 50% POT into the future.

2.       System 2 – it also has a winning strike rate of 20% but long term it has only made 5% POT, it is also expected to continue to make just the 5% POT.

If you had 1000 bets from each system over the course of the next year, then which system would you expect to have had the longest consecutive losing sequence?

You could be excused for choosing System 2 as it has the lower POT, but in fact both systems can expect to encounter the same consecutive losing sequence of 31 bets.

The reason for this is that the expected losing sequence (ELS) is only dependent on the winning strike rate and the number of bets, it has nothing to do with the winning dividend or profitability of a System.

Consider a case where you had a $1 bet on a six coming up on every roll for 1000 rolls of a fair dice, it doesn’t matter if the operator is paying you odds for each six of 2/1 (50% loss on turnover), 5/1 (breakeven) or 8/1 (50% POT) as that will not affect your ELS which in this case will be 38. Obviously, the dividend will make a difference to your overall profitability, but that is not the point of this article.

The point being emphasised is that even with a profitable system, you have to expect (as it will happen) a consecutive losing sequence that is dependent only on the long-term winning strike rate of that system and it is imperative that you manage your bankroll (and head) accordingly. Obviously, you also need to continue to monitor whether the “edge” still exists but knowing the variance you can expect to encounter over a long series of bets helps with this monitoring.

Finally, if you had (or subscribed to) a System that has a great record of long-term profitability and a strike rate of 20% you will certainly at some stage (or if you are extremely unlucky then initially) back 31 consecutive losers. It is easier to handle that mentally and stick to your guns if you both expect it (as it will happen) and you have prepared in advance to manage your bankroll accordingly. 

ELS = LN(#bets)/-LN(1-SR)

LN - Loge

#bets – number of bets

SR – Strike Rate

We recommend you read the next article in this series - The Mathematics of runs of outs and losing streaks: The Mathematics - Runs of Outs or losing streaks